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Proof step 12 from proof inv-link (previous step)

files[dirs[ino].entries[str]] = mkfile(m0, md1, # links(dirs[ino].entries[str], dirs), content), c_inode = mkinode(dirs[ino].entries[str], md0, false, # links(dirs[ino].entries[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size), afs-cons(dirs, files), ino ∈ dirs, str ∈ dirs[ino].entries, m ∈ dirs, dirs[ino].entries[str] ∈ files, ¬ str0 ∈ dirs[m].entries, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
files[dirs[ino].entries[str]] = mkfile(m0, md1, # links(dirs[ino].entries[str], dirs), content), dirs[m] = mkdir(m1, md2, m2, m4, entries), c_inode = mkinode(dirs[ino].entries[str], md0, false, # links(dirs[ino].entries[str], dirs), 0, m3), new_dent = negdentry(str0), p_inode = mkinode(m, md, true, m2, m4, m1), afs-cons(dirs, files), dirs[ino].entries[str] ∈ files, m ∈ dirs, str ∈ dirs[ino].entries, ino ∈ dirs, links(dirs[ino].entries[str], dirs) ≠ ∅ ∨ dirs[ino].entries[str] = ROOT_INO, links(m, dirs) ≠ ∅ ∨ m = ROOT_INO, links(ino, dirs) ≠ ∅ ∨ ino = ROOT_INO ⊦ ⟪afs_link#(mkdentry(str, dirs[ino].entries[str]); p_inode, c_inode, new_dent, err, dirs, files; asynced)⟫ afs-cons(dirs, files), str0 ∈ entries

Rule argument

spec: abstract-dir name: elim seq: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries) subst: [ad, m, md, m0, m1, entries] → [dirs[m], m1, md2, m2, m4, entries]

Additional information

Used simplifier rules: ⊦ ( ((m = ad.size ∧ md = ad.meta) ∧ m0 = ad.nlink) ∧ m1 = ad.nsubdirs) ∧ entries = ad.entries ↔ ad = mkdir(m, md, m0, m1, entries); (elim) Used terms: dirs[m], m1, md2, m2, m4, entries